Show which of the following points is part of the solution set for the inequality y≤25x+1

Question

.(1 point)
Responses

(−10,6)
left parenthesis negative 10 comma 6 right parenthesis

(10,5.5)
left parenthesis 10 comma 5.5 right parenthesis

(10,4)
left parenthesis 10 comma 4 right parenthesis

(10,6)

Answer 1

To determine which points are part of the solution set for the inequality \( y \leq 25x + 1 \), we need to check each point to see if it satisfies the inequality.

1. For the point \((-10, 6)\): \[ y \leq 25(-10) + 1 \ 6 \leq -250 + 1 \ 6 \leq -249 \quad \text{(False)} \]

2. For the point \((10, 5.5)\): \[ y \leq 25(10) + 1 \ 5.5 \leq 250 + 1 \ 5.5 \leq 251 \quad \text{(True)} \]

3. For the point \((10, 4)\): \[ y \leq 25(10) + 1 \ 4 \leq 250 + 1 \ 4 \leq 251 \quad \text{(True)} \]

4. For the point \((10, 6)\): \[ y \leq 25(10) + 1 \ 6 \leq 250 + 1 \ 6 \leq 251 \quad \text{(True)} \]

Conclusion:

The points \((10, 5.5)\), \((10, 4)\), and \((10, 6)\) are part of the solution set for the inequality \( y \leq 25x + 1 \). The point \((-10, 6)\) is not part of the solution set.